Warm-up Exercise

1. Warm-up Exercise • Think-trio-share: measure the length of your physics textbook using the ruler or tape provided. • An infant crawls 5 m east, then 3 m north, then 1 m east. Find the magnitude of the infant’s displacement. • In last week's Homecoming victory, Al Konfurance, the star halfback of South's football team, broke a tackle at the line of scrimmage and darted upfield untouched. He averaged 9.8 m/s for an 80-yard (73 m) score. Determine the time for Al to run from the line of scrimmage to the end zone.

2. Acceleration • Acceleration is a vector quantity which is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. Average acceleration ( a ) = Δv/Δt = (vf-vi) / (tf-ti) • If an object is slowing down, then its acceleration is in the opposite direction of its motion. • Quick Quiz 2.2 (pp.31)

3. Describing Motion with Diagrams • Quantitative graphing – a. The slope of the straight line joining two points on a position vs. time graph is equal to the b. The slope of the line tangent to the position vs. time graph at any given time is defined as average velocity (v) instantaneous velocity

4. Describing Motion with Diagrams • Quantitative graphing – a. The slope of the straight line joining two points on a velocity vs. time graph is equal to the b. The slope of the line tangent to the velocity vs. time graph at any given time is defined as average acceleration ( a ) instantaneous acceleration

5. Exercise Mr. H started 1.0 meter from the front of the room, walking quickly to the back of the lab, picks up the strobe and returns to the middle of the classroom. The position-time graph below represents his motion. Use the graph to answer the next several questions a) a. What is the total distance walked by Mr. H during these 8.0 seconds?b. What is the average speed of Mr. H during these 8.0 seconds?c. What is the average velocity of Mr. H during these 8.0 seconds? d. How fast did Mr. H walk during the first 5.0 seconds?e. How fast did Mr. H walk during the last 3.0 seconds?

6. Constant Acceleration • When an object moves with constant acceleration, the instantaneous acceleration at any point at a time interval is equal to the value of the average acceleration over the entire time interval • A freely falling object is under the influence of gravity alone, regardless of its initial motion, therefore the free-fall acceleration is constant, g=9.80 m/s2, always downwards.

7. Equations for constant acceleration motion Five kinematics quantities: Δx, v0, v, a, and Δt Missing variable a x v v0 t Δx = v.t = (v+ v0)/2 . t v= v0 + at Δx =x -x0 = v0t + ½ at2 Δx =x -x0 = vt - ½ at2 v2 = v02 +2a(x-x0) In most cases, we can set up the frame of reference so that x0=0

8. Equations for constant acceleration motion • v0 – initial velocity for a motion segment; • v – final velocity for a motion segment; • a – acceleration during that motion segment; • Δx – displacement resulted from that motion segment; • t – time for that segment of motion to take place; ALL parameters (except t ) are vector quantities!!!! Question: How to divide motions into proper segment?

9. Exercise Renatta Gas did it again. She failed to fill up her tank during the last four weeks. The velocity-time graph below represents the last six seconds of motion her car before being stranded on a highway in route to her university. Use this graph to determine... a. ...the acceleration of Renatta's car.b. ...the distance traveled during her last 6.0 seconds of motion.

10. Graphic Problem-solving strategy • Always look at a graph’s axis first!!!! • Don’t assume one box is one unit. Look at the numbers on the axis. • The slope of an x vs. t graph gives , the slope of a v vs. t graph gives . • The area under a v-t graph gives , The area under an a-t graph gives • . (Not just limited to linear graphs). velocity acceleration displacement the change in velocity

11. Word Problem-solving Strategy pp36. Green Box Think-pair-share Hayden and Matthew are riding around the neighborhood on their scooters. Hayden is at rest when Matthew passes him moving at a constant speed of 0.37 m/s. After 1.8 seconds, Hayden decides to chase after Matthew, accelerating at 0.91 m/s/s. How much time must Hayden accelerate before he is side-by-side with Matthew?

12. Describing Motion with Diagrams • Qualitative graphing: make sure you differentiate between position vs. time, velocity vs. time and acceleration vs. time!!! • Quick Quiz 2.3, 2.4, 2.5 v X t t

13. v X X C D v A B t t t t v v H X X G E F t t t t X v v X I L J K t t t t

14. Warm-up Exercise The position-time graph below represents the motion of South's basketball coach during the last sixteen seconds of overtime during this past weekend's game. a. Determine the total distance walked by the coach during these 16 seconds.b. Determine the resulting displacement of the coach during these 16 seconds. c. Determine the displacement of the coach after 12.0 seconds.d. At what time did the coach have the greatest displacement from his starting position?e. What was the fastest speed which the coach walked during any of the time intervals for the last 16.0 seconds?f. What was the average speed of the coach for these 16.0 seconds?